The Encyclopedia of Economic Principals

Chapter 42

Platforms, Multi-Homing, Envelopment, and Digital Ecosystems

Price the reach only you deliver, and find the complement that binds.

Four of the chapter's worked examples, made interactive: the competitive bottleneck, multi-homing, moving ecosystem constraints and a cross-side fixed point. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

The competitive bottleneck

What can a platform charge vendors for access to its commuters?

A platform with exclusive users controls the only route to them, so it can charge up to their full value. Overlap removes that exclusivity.

Equation, written in LaTeX: 600(0.07)=42

Equation, written in LaTeX: 42-32-4=6.

Equation, written in LaTeX: 150(0.07)=10.50,

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Each platform has 600 commuters. A vendor earns 0.07 dollars per commuter reached, pays the listing fee and 4 dollars of integration. Overlap is the number of South commuters also active on North.

Predict first. When overlap rises, does the vendor's margin per commuter change, or its reach?

Your prediction

Choose an example

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Figure: The competitive bottleneck. Two bars: the value of 600 new commuters, $42.00, against the fee plus integration, $36.00.
South commuters also on North: 0, Listing fee: $32
Constructed example: the chapter's hypothetical commuter marketplace (600 commuters, 0.07, fee 32, integration 4, overlap 450, maximum fee 6.50); overlap 225 and a fee of 20 are added.

Calculated values

New commuters reached
600
Gross value
$42.00
Payoff from adding South
$6.00
Maximum fee
$38.00
Vendor adds South
yes

With 0 South commuters already on North, adding South reaches 600 new commuters worth 600 x 0.07 = 42.00 dollars. The payoff is 42.00 - 32.00 - 4 = 6.00 dollars, so the vendor adds South. The most South can charge is 42.00 - 4 = $38.00.

Worked steps

  1. Unique reach = 600 - 0 = 600
  2. Gross value = 600 x 0.07 = 42.00
  3. Payoff = 42.00 - 32.00 - 4 = 6.00
  4. Maximum fee = 42.00 - 4 = 38.00

Use the idea

Price access by the unique reach you deliver, not by your total user count.

Where the conclusion applies

Identical vendors, a constant margin per commuter and no value from reaching a commuter twice.

Check your understanding: At overlap 225 and a fee of 20, does the vendor add South?
375(0.07) = 26.25, and 26.25 - 20 - 4 = 2.25 > 0, so yes.

Chapter 42 source: section "Competitive bottleneck in two-sided markets".

Demonstration 2 of 4

Multi-homing needs unique reach and low duplication cost

When does a restaurant list on a second platform?

Adding a platform pays only for the diners it adds. Duplication cost and unique reach are separate margins and both must be favourable.

Equation, written in LaTeX: 90(0.40)-12-h=24-h.

Equation, written in LaTeX: 50(0.40)-12-h=8-h.

Equation, written in LaTeX: 15(0.40)-12-5=-11.

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Platform A reaches 90 diners and B 50. A restaurant earns 0.40 per reachable diner, pays 12 per listing and integration cost h per platform. Overlap counts B's diners also active on A.

Predict first. At overlap 35, can cutting integration cost to 1 restore multi-homing?

Your prediction

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Figure: Multi-homing needs unique reach and low duplication cost. Bars of the payoff from adding platform B at integration costs 1, 5 and 9 with 50 new diners.
Integration cost per platform: 5, B diners also on A: 0
Constructed example: the chapter's hypothetical restaurant platforms (90 and 50 diners, 0.40, listing 12, h of 1, 5 and 9, overlap 35); every input is the book's.

Calculated values

New diners from B
50
Payoff from adding B
$3
Multi-homes
yes
Largest overlap that still pays
7.5

After joining A, B adds 50 new diners, so adding B pays 50 x 0.40 - 12 - 5 = 3 dollars. The restaurant multi-homes. At h = 5, adding B pays only while (50 - overlap)(0.40) >= 17, that is overlap at most 7.5.

Worked steps

  1. New diners = 50 - 0 = 50
  2. 50 x 0.40 = 20.00
  3. 20.00 - 12 - 5 = 3.00
  4. Overlap limit: 50 - 17 / 0.40 = 50 - 42.5 = 7.5

Use the idea

Before subsidizing integration tools, check that the second platform still brings enough unique customers.

Where the conclusion applies

A constant contribution per diner and no value from reaching the same diner on two platforms.

Check your understanding: At h = 1, how much overlap can the restaurant tolerate?
(50 - o)(0.40) - 13 >= 0 gives o <= 17.5, so at most 17 overlapping diners.

Chapter 42 source: section "Multi-homing in two-sided markets".

Demonstration 3 of 4

Ecosystem constraints move

Which intervention raises adoption when four complementary activities must all be ready?

Under the essential-activity rule only the smallest readiness share matters. Improving any other activity does nothing until the binding one moves.

Equation, written in LaTeX: A=200\min\{0.92,0.55,0.80,0.70\}=110.

Equation, written in LaTeX: A'=200\min\{0.92,0.75,0.80,0.70\}=140.

Equation, written in LaTeX: A''=200\min\{0.92,0.75,0.80,0.85\}=150.

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200 buildings could adopt. Readiness shares are equipment 0.92, installers 0.55, permits 0.80 and finance 0.70. Training lifts installers to 0.75 for 15,000 dollars; finance can rise to 0.85. Each completed retrofit contributes 900 dollars.

Predict first. Does the finance agreement alone raise adoption?

Your prediction

Choose an example

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Figure: Ecosystem constraints move. Four readiness bars (0.92, 0.55, 0.80, 0.70); installers is the lowest and sets adoption at 110 of 200 buildings.
Installer training: Off, Finance agreement: Off
Constructed example: the chapter's hypothetical retrofit programme (readiness 0.92, 0.55, 0.80, 0.70; training to 0.75; finance to 0.85); finance on its own is added.

Calculated values

Binding activity
Installers
Completed adoption
110
Extra installations
0
Contribution from extra installations
$0
Training cost
$0
Net of training cost
$0

A = 200 min{0.92, 0.55, 0.80, 0.70} = 200 x 0.55 = 110, with installers binding. That is 0 more installations than 110, worth 0(900) = $0; less training cost $0 leaves $0.

Worked steps

  1. min{0.92, 0.55, 0.80, 0.70} = 0.55 (installers)
  2. A = 200 x 0.55 = 110
  3. Extra = 110 - 110 = 0
  4. 0 x 900 - 0 = 0

Use the idea

Find the binding complement first, and expect the next one to bind after you relieve it.

Where the conclusion applies

Activities are perfect complements and readiness shares are independent of each other.

Check your understanding: With training and finance both on, what binds next?
min(0.92, 0.75, 0.80, 0.85) = 0.75, installers again; 200(0.75) = 150.

Chapter 42 source: section "Complementary Assets and the Ecosystem Effect".

Demonstration 4 of 4

Subsidize one side, gain on the other

Does a user discount pay for itself through the developers it attracts?

A lower price on one side draws participants, which raises the other side's value and feeds back. The fixed point is where the two response lines meet; the discount's cost grows with the users it attracts.

Equation, written in LaTeX: n_U=100(4+0.01n_D-p_U), n_D=10(2+0.005n_U-p_D).

Equation, written in LaTeX: n_U=\frac{100}{0.95}\approx105.26, n_D\approx5.26.

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n_U and n_D are user and developer participation; p_U and p_D are their prices, with 4 and 2 as the starting prices. Each developer is worth 30 dollars of future contribution, and a discount costs its size times participation.

Predict first. Does a two-dollar user discount pay twice as well as a one-dollar discount?

Your prediction

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Figure: Subsidize one side, gain on the other. User and developer response lines meet at 105.26 users and 5.2632 developers for prices 3 and 2.0.
User price: 3, Developer price: 2
Constructed example: the chapter's hypothetical developer platform (prices 4 and 3 for users, 2 for developers, 30 per developer); a user price of 2 and a developer price of 1.5 are added.

Calculated values

Users n_U
105.26
Developers n_D
5.2632
Developer-side value
$157.89
Cost of user discount
$105.26
Cost of developer discount
$0.00
Net cross-side gain
$52.63

At p_U = 3 and p_D = 2.0 the relations are n_U = 100 + n_D and n_D = 0 + 0.05 n_U, so 0.95 n_U = 100 and n_U = 105.26, n_D = 5.2632. Developers are worth 30 x 5.26316 = $157.89; the discounts cost $105.26 on users and $0.00 on developers, leaving $52.63. The book rounds n_D to 5.26 before multiplying; the exact values are shown here.

Worked steps

  1. n_U = 100 + n_D; n_D = 0 + 0.05 n_U
  2. n_U = (100 + 0) / 0.95 = 105.26316
  3. n_D = 0 + 0.05 x 105.26316 = 5.26316
  4. Developer value = 30 x 5.26316 = 157.89
  5. Discount costs = 1 x 105.26316 + 0.0 x 5.26316 = 105.26
  6. Net = 157.89 - 105.26 = 52.63

Use the idea

Value a subsidy by the fixed point it produces, and compare the cross-side value with the discount paid on every subsidized participant.

Where the conclusion applies

Linear local responses, negatives set to zero and a constant 30 dollars per developer. The book's accounting uses n_D rounded to 5.26 (157.80 and 52.54); the exact values 157.89 and 52.63 are shown.

Check your understanding: At p_U = 3 and p_D = 1.5, what are participation levels?
n_U = 100 + n_D and n_D = 5 + 0.05 n_U, so 0.95 n_U = 105, n_U = 110.53 and n_D = 10.53.

Chapter 42 source: section "Two-Sided Markets, Switching Costs, and Viral Adoption".